1. Field of the Invention
This invention generally relates to an airborne or a spaceborne ocean scatterometer for use in global wind measurements over an ocean surface. More specifically, the present invention relates to an apparatus and method for sensing and processing reflected global positioning system (GPS) signals from an ocean surface for wind measurements in a wide range of altitudes and conditions.
2. Description of Related Art
Monostatic scatterometers have been used to measure, with a high degree of accuracy, a surface backscatter cross section relating to the surface roughness at the scale of the observing wavelength. In particular, the backscatter measurements have been employed to acquire information about wind velocity over an ocean surface. For instance, as the wind blows over the ocean surface, it generates and amplifies surface waves due to the resonant coupling between the turbulent fluctuations in the air and the water surface. Since wind velocity is proportional to the roughness of the ocean surface, the wind velocity can be determined by tracking reflected signals from the ocean surface. Another type of a scatterometer is a bistatic scatterometer. It uses a transmitter and receiver separated by a significant distance and records the forward quasi-specular scatter from the transmitter in the direction of the receiver. This type of scatter provides information about surface slope statistics which is related to the surface wind vector. This information cannot be obtained by conventional backscatter (monostatic) scatterometer.
The following references provide background information relating to ocean scatterometers and are hereby incorporated by reference:
(1) S. F. Clifford, V. I. Tatarskii, A. G. Voronovich, and V. I. Zavorotny, GPS Sounding of Ocean Surface Waves: Theoretical Assessment, Int. Geosci. Remote Sensing Symp. Proc., Seattle, Wash. July 1998; PA1 (2) S. J. Katzberg and J. L. Garrison, Jr., Utilizing GPS to determine ionospheric delay over the ocean, NASA Technical Memorandum, December 1996; PA1 (3) J. L. Garrison, S. J. Katzberg and C. T. Howell, Detection of ocean reflected GPS signals: theory and experiment, IEEE Southeastcon '97 "Engineering the New Century, April 1997; PA1 (4) M. Martin-Neira, A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry, ESA Journal, Vol.17, No.4, pp. 331-355, 1993; PA1 (5) U.S. Pat. No. 5,546,087; PA1 (6) T. Gruber, The CHAMP mission and its capabilities to recover the ocean surface from reflected GPS signals, Ionospheric Determination and specification for Ocean Altimetry and GPS Surface Reflections Workshop, Jet Propulsion Laboratory, December 1997; PA1 (7) K. D. Anderson, A Global Positioning System (GPS) tide gauge, AGARD SSP Specialists Meeting, Remote Sensing, Toulouse, France, Apr. 22-25, 1996, Paper No. 32, 1996; PA1 (8) James L. Garrison and Stephen J. Katzberg, Effect of sea roughness on bistatically scattered range coded signals from the Global Positioning System, Geophysical Research Letters, Vo. 25, No. 13, pp. 2257-2260, Jul. 1, 1998. PA1 (9) C. Elachi, Spaceborne Radar Remote Sensing: Applications and Techniques, IEEE Press, New York 1988; PA1 (10) F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive, vol. 2, Addison-Wesley Reading, Mass. 1982; PA1 (11) B. W. Parkinson, J. J. Spilker, P. Axelrad, and P. Enge (Eds.), Global Positioning System: Theory and Applications, American Institute of Aeronautics and Astronautics, vol. 1, pp. 793, 1996; PA1 (12) S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics, Springer-Verlag, Berlin, Vol. 4, 1988; PA1 (13) J. R. Apel, An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter, J. Geophys. Res., vol. 99, pp. 269-291, 1994; and PA1 a pseudo-random noise code in code-chip length (.tau..sub.c); PA1 b replica of pseudo-random noise code in code-chip length (.tau..sub.c); PA1 c speed of light; PA1 f frequency; PA1 h GPS receiver altitude; PA1 j,m,n variables representing certain fixed numbers; PA1 q scattering vector value; PA1 s slope variance; PA1 t moment; PA1 x,y,z spherical coordinates; PA1 D Doppler shift; PA1 F footprint; PA1 I inphase component; PA1 Q quadrature component; PA1 R,R.sub.0 range from GPS transmitter/receiver to scattering surface; PA1 T time; PA1 Y received signal correlation; PA1 .theta. grazing angle; PA1 .LAMBDA. triangle function; PA1 .sigma. differential backscattering coefficient; PA1 .tau. time delay (interval or time duration of one C/A chip); and PA1 .rho. integration point (variable) on surface.
Additionally, the following symbols and definitions are typically used to illustrate conventional GPS bistatic scatterometers:
Atomospheric profiles may be obtained at a modest cost if GPS direct signals are efficiently utilized by space-borne receivers. For instance, the existing net of 24 Navigation Satellite Timing And Ranging (NAVSTAR) satellites have been tested for use in ocean altimetry, wind scatterometry, and ionospheric sounding by receiving GPS signals scattered from the Earth's land and ocean surface (see references 1-8). GPS satellite transmitters emit a phase-code modulated signal with a highly stable carrier 24 hours a day practically above any point on the planet. Various conventional GPS bistatic scatterometers which deploy GPS receivers on, e.g., airplanes, low-orbiting satellites or an elevated ocean coast have been disclosed, for instance, in references 2-8. The conventional radar remote sensing techniques used in the conventional bistatic radar-scatterometer for extracting information about surface characteristics with elements of a synthetic aperture radar (see, e.g., references 9 and 10) have been employed in the conventional GPS bistatic scatterometers. The peculiarity of the conventional GPS bistatic scatterometer is that its forward-scatter character provides information regarding an ocean surface which is complimentary to that obtained from other conventional backscatter scatterometers.
References 3 and 8 disclose, through pioneering experiments, that the scattering of GPS signals from the ocean surface can be detected by a specially designed Plessey GPS receiver. Reference 6 discloses plans to launch satellites with GPS receivers on-board to track GPS signals reflected off the ocean surface to investigate the possibility of ocean altimetry and scatterometry. Based on mathematical calculations, however, reference 1 shows that the Plessey-type receiver with a low-gain, wide-beam antenna must operate at altitudes of 5 to 15 kilometers (km) to yield decent results. For instance, for an orbit platform of 300 km, calculations (even with the assumption of a full Doppler-shift compensation) give the reflected signal level (normalized to the direct signal) less than -20 decibels (dB). Additionally, for the Plessey-type receiver at lower than 5 km altitudes, the receiver cannot provide enough sensitivity to the wind speed because of the too coarse spatial resolution of this system (see reference 1).
A conventional GPS scatterometer having an one-chip limited footprint is discussed hereinbelow. Referring to a conventional GPS transmitter, the wide-beam antenna of the GPS satellite emits right-hand circularly polarized electromagnetic waves. The temporal structure of the GPS direct signal is quite complicated (see reference 11). It consists of two highly stable almost monochromatic carriers, L1 and L2, upon which three modulations are impressed: the C/A code, the P-code, and the broadcast message. All components of the GPS signal are based upon the fundamental clock rate f.sub.0 of 10.23 MHz. The GPS carriers L1 and L2 are f.sub.c,2 =154f.sub.0 for L1 and f.sub.c,2 =120f.sub.0 for L2.
The method of modulating the carrier is a binary biphase modulation. The two codes are pseudo-random noise (PRN) codes. The P-code is at the modulation frequency f.sub.m,P =f.sub.0, and the C/A code is at f.sub.m,C/A =f.sub.0 /10. According to these frequencies a binary biphase modulation function a(t) acquires values either 1 (normal state) or -1 (mirror image state). These states of the modulation function are called "chips" rather than bits to indicate that they do not carry data. One chip lasts for a time period of .tau..sub.c =1/f.sub.m, and has length .DELTA.=c.tau..sub.c. The carrier is modulated by multiplying it by a(t). Each transition of a(t) from +1 to -1 or from -1 to +1 leads to a 180.degree. phase shift of the carrier. This modulation spreads the signal over a wide bandwidth, and it is usually referred as a spread-spectrum technique. The advantages of using this technique are found in, e.g., reference 11.
The signal u(t.sub.0) obtained from the antenna output at a moment t.sub.0 after the Doppler shift compensation is convolved with a replica of PRN code-modulation function a(t) taken at a different time moment t.sub.0 +.tau.: ##EQU1## In the case of a direct signal, u(t) is simply proportional to a(t) taken with some time offset t.sub.off caused by the propagation from the transmitter to the receiver. Because the GPS receivers described in references 2-8 are based on C/A code allowed for a civilian use, the function a is equal to +1 or -1 within the time interval .tau..sub.c or "chip," equal to about 1 .mu.s. In the spatial domain the chip length is about 300 m. The procedure in equation (1) is used to dispread the signal and to find the time offset t.sub.off for navigational purposes. This procedure is called code correlation because the correct time offset t.sub.off is achieved by cross-correlating the received signal with the code replica a (see FIG. 1-A). A time elapse is required to search for the maximum correlation by repeating this procedure many times for different time delays. The maximum correlation indicates that the two codes are aligned. Once the maximum is found, then the signal integrating starts. Finally, the signal level depends on the integration time T.sub.1.
Referring to the conventional method of generating the one-chip-limited footprint, the GPS bistatic scatterometer uses the GPS transmitter of opportunity and the GPS receiver of the scattered signal (see, e.g., the GPS airborne receiver described in references 3 and 8). Schematically, the hardware consists of two receivers configured so that one received the GPS signal in the conventional manner using a right-hand circularly polarized (RHCP) antenna on top of the airplane fuselage. This up-looking channel collects all needed navigational information and controls the other down-looking channel, which receives the scattered signal using an antenna on the bottom of the fuselage which is LHCP because of polarization change in the scattered signal. The main purpose of this receiver is to record the signal level. The uplooking receiver is programmed to track the six highest zenith angle satellites visible, and the downlooking receiver provides six "daughter" channels which look for reflected signals from the same six satellites that their uplooking "mothers" are tracking. Because the GPS satellite, the GPS receiver, and scattering surface itself are moving with respect to each other, the carrier frequency of scattered signal acquires an additional Doppler shift which tends to be different for different parts of the scatter surface. The conventional GPS receiver provides the possibility to annul the Doppler shift, but only for one specific value .delta.f in a time.
The signal obtained from the down-looking antenna output u(t.sub.0) at a moment t.sub.0 is convolved with a replica of PRN code-modulation function a(t) taken at a different time moment t.sub.0 +.tau. using the same procedure as in equation (1). However, there are some important differences. In the case of a signal scattered from a surface (see FIG. 2), u(t) is proportional to the surface integral from a(t,r) rather than to the a(t) itself: EQU u(t)=.intg.a[t-(R.sub.0 +R)/c]g(r,t)exp[2.pi.i(f.sub.c -f.sub.D (r))t]d.sup.2 r (2)
In this instance, the stochastic function g(r,t) describes the instantaneous effect of the surface scattering (see, e.g., reference 12). The term in the exponent describes the frequency misalignment between the compensation frequency offset f.sub.c and the Doppler shift f.sub.D, where f.sub.D =(v.sub.0 .multidot.R.sub.0 /R-v.multidot.R/R)/.lambda.) shift is caused by the receiver and transmitter motions with respect to the Earth's surface. The vector R.sub.0 is the distance vector pointing from the transmitter to the integration point p on the surface and R is the distance vector pointing from that surface point to the receiver; v.sub.0 and v are the velocity vectors of the transmitter and the receiver, respectively. In this instance, the Earth's rotation speed and the possible hydrodynamic speed of the water surface are neglected. The mean surface position is at z=0 with z-axis directed upward, and a transmitter and receiver located in the (x,z)-plane (see FIG. 2). The integration in the right-hand part is performed over the mean-level surface of the ocean.
It follows from equation 2 that the signal u(t.sub.0) at a given time moment t.sub.0 is composed of the a(t) functions taken at different moments t=t.sub.0 -(R.sub.0 +R)/c. Because of a variety of distances R.sub.0 +R, points on the surface can be found for which the procedure in equation (1) gives a maximal signal Y. These points corresponds to the situation when a(t.sub.0 -t-.tau.) from equation (1) exactly matches a[t.sub.0 -(R.sub.0+ R)/c] from equation (2). This situation is depicted in FIG. 1-B where signals u.sub.1,u.sub.2, etc., denote partial contributions from surface zones with various distances R.sub.0 +R that simultaneously reach the antenna at some moment t. In FIG. 1-B the situation is shown where the replica a aligns (correlates) only with the contribution u.sub.2. Therefore, the mean surface itself creates a correlation processor transforming range delays into temporal delays. The important feature of this processor is that zero time is needed to find the maximal correlation because the alignment of the code a from the signal and its replica always happens for the appropriate spatial zone on the surface. The position of this zone is easily predicted from the navigation information obtained from the direct GPS channel.
The final output of the GPS receiver is the power averaged over time T.sub.2 &gt;&gt;.tau..sub.c as a function of a time delay .tau. which is proportional to the value of &lt;.vertline.Y(.tau.).vertline..sup.2 &gt;=&lt;I.sup.2 (.tau.)&gt;+&lt;Q.sup.2 (.tau.)&gt;, where I and Q are inphase and quadrature components of the signal Y. The block diagram of the one-chip GPS receiver of a scattered signal is depicted in FIG. 3.
In particular, FIG. 3 shows a PRN code replica generator 32 for generating a replica of the pseudo-random noise (PRN) codes, which is passed through a discrete delay device 34 with an output to one of the two inputs in a code correlator 35. The other input of the code correlator receives reflected GPS signals thorough a receiving antenna 36. The code correlator 35 correlates the delayed replica of the PRN codes with the reflected signal. The output of the code correlator 36 is processed by an average power integrator to generate an averaging power signal over time T.sub.2 &gt;&gt;.tau..sub.c. The average power signal is further processed by a signal processor (not shown) to derive data on wind conditions such as wind velocity vectors.
By making use of the Kirchoff approximation and assuming that T.sub.2 is much smaller than the typical correlation time caused by the surface statistics (i.e., a "frozen"-surface assumption), the average power can be expressed as: ##EQU2## The integration in the right-hand part is performed over the mean-level surface of the ocean. Equation (3) has a form of a bistatic-radar equation with the function F.sup.2 as a radar footprint, and with the function .sigma..sub.0 as the scattering cross-section of the sea-surface. This function originates from auto-correlation of the stochastic function g(r,t) in equation (2). In the case of diffusive scattering (i.e., the Rayleigh parameter is large, q.sub.2 .sigma..sub..zeta. &gt;&gt;1), the geometrical optics limit can be represented as: EQU .sigma..sub.0 =.pi..vertline.V.vertline..sup.2 (q/q.sub.z).sup.4 W(-q.sub..perp. /q.sub.z (4)
where V is the polarization-dependent Fresnel reflection coefficient; q=K(R/R-R.sub.0 /R.sub.0) the scattering vector, and W is the probability density function of surface slopes. For example, for isotropic Gaussian slopes it is described by EQU W(s)=(1/.pi.&lt;s.sup.2 &gt;)exp(-s.sup.2 /&lt;s.sup.2 &gt;) (5)
with the total slope variance .sigma..sub.s.sup.2 .ident.&lt;s.sup.2 &gt;=&lt;s.sub.x.sup.2 &gt;+&lt;s.sub.y.sup.2 &gt;.
The footprint function F appears in equation (3) in a result of the code-convolution process in equation 1: ##EQU3## This function can be approximated by the product of two functions EQU F(r,.tau.).apprxeq.T.sub.1 .LAMBDA.[.tau.-(R.sub.0 +R)/c]D(r)(7)
where ##EQU4## The function A has the shape of a triangle with the base 2.tau..sub.c (see FIG. 4). It is equal to zero for .vertline..tau..vertline.&gt;.tau..sub.c and ##EQU5## It includes into integration in equation (3) only the part of a surface which satisfies the condition .vertline..tau.-[(R.sub.0 +R)/c].vertline.&lt;.tau..sub.c, (i.e., one-chip-footprint). This area has a shape of an elliptic ring (an annulus zone) which expands with .tau.. Elliptic boundaries of the annulus zone are, so-called, iso- or equi-range lines satisfying the condition R+R.sub.0 =const. It means that all GPS signals scattered from points located on an ellipsoid of a rotation (having the transmitter and the receiver in its foci) experience the same delay time. The intersection of this ellipsoid with the surface is approximately an ellipse. In practice .tau. is large enough to compensate a bulk delay caused by a signal propagation from a transmitter to a receiver.
Referring to the Doppler shift and corresponding Doppler zones as shown in FIG. 2, points located on coaxial cones, with the line connecting the receiver and the transmitter as the axis and the receiver a the apex, have returned echoes with identical Doppler shifts. The intersection of these cones with the surface plane gives a family of hyperbolas. Scatterers on a certain hyperbola will provide equi-Doppler returns. The function ##EQU6## describes the zone on the surface limited by to such hyperbolas for which the Doppler-shift differs by about .delta.f=1/2T.sub.1.
Assuming that the Doppler shift is annulled for the entire area of the integration in equation (3), the annulus zone would turn to the footprint zone. This occurs for relatively slow moving and low flying platforms as airplanes. For satellite altitudes and speeds, the width of the Doppler zone can be smaller than both the glistening zone and annulus zone. Generally, the footprint is described by the function F in equation (7) or (8), and is the area of the intersection of the Doppler zone and the annulus zone (see areas A and B in FIG. 2). The level of the received signal is roughly proportional to the ratio between the footprint area and the glistening zone area. With increasing the glistening zone and decreasing the footprint the received signal is dropping. Therefore, for the given transmitted power, the area of the footprint is insufficient to produce required level of the scattered signal at the receiver antenna location. One way is to increase the receiving antenna gain. However, this will create the loss of many advantages of the low-gain antenna: the small size, the low weight and cost, the capability to operate with a multiplicity of satellites.
Referring to the limitations on wind retrieval with the one-chip-limited GPS receiver, the performance of the one-chip-limited GPS receiver of scattered signal can be considered under the aspect of wind retrieval if the Doppler shift is assumed to be completely removed for the entire range of the annulus zone. The width .rho..sub.g of .sigma..sub.0 over p determines the glistening zone on the ocean surface. The value of .rho..sub.g is proportional to the receiver altitude h and the R.M.S. slopes .sigma..sub.s. In absence of winds the glistening zone shrinks to the single specular point. At the same time the width of the chip-limited footprint or the annulus zone, .rho..sub.a is proportional to the square root of hc.tau..sub.c. For low receiver altitudes and for low winds, .rho..sub.g can be smaller than .rho..sub.a. Also the Doppler shift can be easily compensated for the entire glistening zone. In this situation the integral in equation (2) can be evaluated by replacing the footprint function F with the annulus function .LAMBDA. the W-function with the .delta.-function. Therefore, any dependence on .sigma..sub.s.sup.2, or wind speed disappears, and it can be concluded that these altitudes are not optimal for wind retrieval. However, there exists a range of altitudes and wind speeds were the relationship between .rho..sub.g and .rho..sub.a is optimal, i.e. .rho..sub.g =.rho..sub.a N, where the number N is close to the number of bins in time-delay sampling over .tau.. It means that for different moments of time delay .tau. (taking a proper time offset) from 0 to some .tau..sub.max the annulus zone will scan through the entire glistening zone, and the dependence of the received signal on e will reflects the shape of this zone. Such optimal process is depicted schematically in FIGS. 5-A through 5-D. With further increase of the receiver height, the width of the glistening zone can become so large such that: (a) for the fixed .tau..sub.max, the center of the glistening zone stays constant, and never reach its periphery, and (b) for fixed .tau..sub.c, the portion of scattered energy intercepted by the annulus zone will decrease with the glistening zone expanded further.
The results of the numerical computations are shown in FIGS. 6-A through 6-C. Curves correspond to the value of the left-hand polarized scattered signal (as a function of .tau.) normalized on the direct signal, P.sub.N (.tau.)=&lt;.vertline.Y(.tau.).vertline..sup.2 &gt;R.sub.d.sup.2 /.LAMBDA..sup.2 (0), where R.sub.d is the distance between the GPS satellite and the receiver. The value of the time offset was chosen to have a maximal signal at .tau.=0 for the case of a perfectly specular reflection from the surface. In the calculations the Gaussian statistics of slopes with non-isotropic surface slope variances &lt;s.sup.2.sub.x &gt;, &lt;s.sup.2.sub.y &gt; are used. These variances are wind-dependent and are derived from a Donelan-Banner spectrum for developed seas (see, i.e., reference 13) by integration over wave numbers smaller than 2.pi., where .lambda.=0.2 m for L1 GPS carrier. Typical values of R.M.S. slope angles a.sub.x,y =atan&lt;s.sup.2.sub.x,y &gt;.sup.1/2 for different values of wind speed at 10 m height are: for U.sub.10 =4 m/s: a.sub.x =4.7.degree. and a.sub.y =3.3.degree.; for U.sub.10 =10 m/s: a.sub.x =6.6.degree. and a.sub.y =5.5.degree.; for U.sub.10 =20 m/s: a.sub.x =7.8.degree. and a.sub.y =7.0.degree..
The curves are calculated for the case of the 90.degree. GPS elevation angle and the 0.degree. wind direction. Trailing edge slopes in FIGS. 6-A and 6-C demonstrate lower sensitivity to wind speed than in FIG. 6-B. One can see that for low and high altitudes the situation for the wind retrieval is unfavorable.
The theoretical assessment (see reference 1) of the performance of the GPS bistatic scatterometer with low-gain, wide-beam antenna described in, e.g., references 2, 3 and 8 shows that the signal scattered from the ocean surface and received by such system is sensitive to the typical surface wind speed only for some limited interval of altitudes h of the receiving antenna, around 10 km. The performance of the mentioned GPS scatterometer is not optimal for lower and higher altitudes. Particularly for satellite altitudes, the level of signal is typically less than -20 dB. If limitations caused by the Doppler shift are taken into account, then this number would be reduced even more. To suppress those negative factors suggestions were made (see reference 4) to use high-gain, narrow-beam antennas. However, this would eliminate many of advantages of GPS receivers with low-gain antennas: the low cost, size and weight; the simultaneous access to several GPS satellites; the operational robustness.